Question

plz solve in step
its urgent

Answer 1

given,
p(x) = x^3 - 2x^2 + 3x - 1
g(x) = x^2 - 1

just put values of g(x) in every x in p(x)...

∴ p(g(x)) = (x^2-1)^3 - 2(x^2 - 1)^2 + 3(x^2 -1) - 1
               = x^6 + 1 + 3x^2(x^2 + 1) - 2(x^4 +1 - 2x^2) + 3x^2 - 3 - 1
               = x^6 +1 + 3x^4 + 3x^2 - 2x^4 - 2 + 4x^2 + 3x^2 - 4
   p(g(x)) = x^6 + x^4 +10x^2 - 5

∴ p(g(1)) = 1 + 1 + 10 - 5 = 7                ...............(1)
   p(-1) = -1 - 2 -3 -1 = - 7                     ...............(2)
   p(1/2) = 1/8 - 2/4 + 3/2 -1 = (1 - 4 + 12 - 8)/8 = 1/8     .....................(3)

∴ p(-1) + p(1/2) - p(g(1)) = - 7 +1/8 - 7
                                       = (- 56 + 1 - 56)/8 
                                       = -111/8 
                                       ≈ -13.875

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